A178769 - OEIS

%I #32 Sep 09 2024 20:03:40

%S 2,7,57,557,5557,55557,555557,5555557,55555557,555555557,5555555557,

%T 55555555557,555555555557,5555555555557,55555555555557,

%U 555555555555557,5555555555555557,55555555555555557,555555555555555557,5555555555555555557,55555555555555555557,555555555555555555557

%N a(n) = (5*10^n + 13)/9.

%H Bruno Berselli, <a href="/A178769/b178769.txt">Table of n, a(n) for n = 0..1000</a>.

%H Bruno Berselli, <a href="http://www.base5forum.it/upload/57_46.gif">A property that includes the numbers of the form 5..57</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n)^(4*k+2) + 1 == 0 (mod 250) for n > 1, k >= 0.

%F G.f.: (2-15*x)/((1-x)*(1-10*x)).

%F a(n) - 11*a(n-1) + 10*a(n-2) = 0 (n > 1).

%F a(n) = a(n-1) + 5*10^(n-1) = 10*a(n-1) - 13 for n > 0.

%F a(n) = 1 + Sum_{i=0..n} A093143(i). - _Bruno Berselli_, Feb 16 2015

%F E.g.f.: exp(x)*(5*exp(9*x) + 13)/9. - _Elmo R. Oliveira_, Sep 09 2024

%t CoefficientList[Series[(2 - 15 x) / ((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)

%t LinearRecurrence[{11,-10},{2,7},20] (* _Harvey P. Dale_, Feb 28 2017 *)

%o (Magma) [(5*10^n+13)/9: n in [0..20]]; // _Vincenzo Librandi_, Jun 06 2013

%o (PARI) vector(20, n, n--; (5*10^n+13)/9) \\ _G. C. Greubel_, Jan 24 2019

%o (Sage) [(5*10^n+13)/9 for n in (0..20)] # _G. C. Greubel_, Jan 24 2019

%o (GAP) List([0..20], n -> (5*10^n+13)/9); # _G. C. Greubel_, Jan 24 2019

%Y Cf. A165246 (..17, 117, 1117,..), A173193 (..27, 227, 2227,..), A173766 (..37, 337, 3337,..), A173772 (..47, 447, 4447,..), A067275 (..67, 667, 6667,..), A002281 (..77, 777, 7777,..), A173812 (..87, 887, 8887,..), A173833 (..97, 997, 9997,..).

%Y Cf. A093143.

%K nonn,easy

%O 0,1

%A _Bruno Berselli_, Jun 13 2010